Integrating Fuzzy Multiobjective Programming and System Dynamics to Develop an Approach for Talent Retention Policy Selection: Case on Health-Care Industry

The demand for medical services has been increasing yearly in aging countries. Medical institutions must hire a large number of staff members to provide efficient and effective health-care services. Because of high workload and pressure, high turnover rates exist among health-care staff members, especially those in nonurban areas, which are characterized by limited resources and a predominance of elderly people. Turnover in health-care institutions is influenced by complex factors, and high turnover rates result in considerable direct and indirect costs for such institutions (Lo and Tseng 2019). Therefore, health-care institutions must adopt appropriate strategies for talent retention. Because institutions cannot determine the most effective talent retention strategy, many of them simply passively adopt a single human resource (HR) policy and make minor adjustments to the selected policy. In the present study, system dynamics modeling was combined with fuzzy multiobjective programming to develop a method for simulating HR planning systems and evaluating the suitability of different HR policies in an institution. We also considered the external insurance policy to be the parameter for the developed multiobjective decision-making model. The simulation results indicated that reducing the turnover rate of new employees in their trial period is the most effective policy for talent retention. The developed procedure is more efficient, effective, and cheaper than the traditional trial-and-error approaches for HR policy selection.


Introduction
Population aging engenders changes in population structure. Terefore, in aging societies, increasing attention has been paid to issues such as medical care, medical economics, psychology, and social welfare policies. Because of the low muscle strength and fexibility of elderly people, considerable resources must be spent on their health care [1]. However, the challenges involved in caring for elderly people impose high pressure on health-care staf, which results in a high staf turnover rate. Accordingly, staf turnover is a major problem facing health-care institutions in aging countries.
Traditionally, medical service providers maintain their competitiveness by hiring professional personnel to minimize care risks as well as human errors in instrument or device operation and medication provision [2]; thus, labor constitutes more than 45% of the total cost incurred by medical institutions. Some hospitals use human resource planning (HRP) strategies involving a hiring freeze to achieve cost reduction and profts. Other hospitals even occasionally adopt the lowest standard of labor as a business strategy. However, hospitals cannot predict the number of patient visits. In addition, a sudden increase in the number of staf members leads to an increase in the burden on the original staf; this is because the original staf must mentor the new staf. Some new staf members might also make mistakes because of insufcient experience, which can negatively afect the reputation of the hospital they work for. Te medical industry is a labor-intensive industry, and cost reduction attempts involving personnel cuts can lead to reduced medical service quality and endanger patients' lives. In addition, a high number of adverse events can occur in a high-burden environment, which increases the rate of human resource (HR) loss. Terefore, cost reduction strategies in the medical industry are associated with moral dilemmas.
Medical institutions must adopt fexible strategies to achieve efective team building and avoid brain drain. In particular, medical institutions can secure their competitiveness by hiring sufcient personnel. Furthermore, when designing HRP strategies, HR planners must consider internal and external factors to ensure that develop comprehensive HR plans and system policy evaluation models from an organizational system perspective.
In the health-care feld, root cause analysis (RCA) is one of the most common methods for systematic policy evaluation. RCA is based on secondary data and analysis data obtained through discussions among individuals with different subjective judgments and professional backgrounds [3]. Terefore, RCA can only produce a consensus decision instead of an objectively correct answer [4]. Moreover, the results of the root cause explanations might difer over time. Tus, it is not suitable for HRP issues. HRP is a complicated process and can be defned as a systematic analysis of HR needs to ensure that adequate numbers of employees with the required skills are available at a given time [5]. Several studies have used statistical techniques and mathematical models to forecast HR demand and supply and to execute HRP. However, because of their fundamental limitations, these techniques and models cannot be used for dynamic structural analysis and the identifcation of delayed feedback efects. Actions undertaken on the basis of inaccurate demand forecasts can occasionally produce results that are contrary to the intended ones. Tus, a systematic tool that can consider complex and dynamic factors must be developed for evaluating HRP policies [6].
In the system dynamics (SD) approach, features such as feedback delays and nonlinear relationships are considered for accurately determining the HR demand and supply. Accordingly, SD modeling is suitable for studying the behavior of a dynamic HRP system [6]. Te system dynamics (SD) approach can deal with forecasting inaccuracies and potential mismatches and towards understanding and policy design, which use dynamic features such as feedback delays and nonlinear relationships are considered by very few modelers to deal with HR demand and supply uncertainties. In order to study the behavior of a dynamic HRP system, SD modeling is an appropriate tool.
Several uncertain factors infuence the medical actions or administrative decisions taken in a health-care institution. Furthermore, such an institution can have multiple goals related to medical personnel, patients, insurance, and the institution. An SD model considers internal and external factors that afect a system and decreases the percentage of wrong decisions; such a model can thus be benefcial for such institutions. Nevertheless, administrative decisions are complex. Terefore, a fuzzy model can facilitate the task of identifying appropriate administrative decisions. In the medical feld, no closed-form solution is generally available for the problem of determining appropriate administrative decisions. Te most reasonable approach for administrative decision-making in the medical feld involves creating a fuzzy set of multiple decision parameters to determine the optimal decision for achieving a goal. Accordingly, the present study combined SD modeling and fuzzy multiobjective programming (MOP) to develop an HRP system for evaluating the appropriateness of diferent HR policies in a health-care institution. Te SD approach was adopted to create complex and nonlinear models to determine causal feedback relationships [6].
Several studies have adopted SD approaches that entail the consideration of an entire system for analysis. Nonetheless, according to our search of the PubMed database, no study has adopted SD modeling for analyzing nursing talent retention policies in medical institutions. Hence, the present study applied SD modeling to examine the suitability of diferent labor policies in medical institutions; the study also adopted a hybrid modeling approach to simulate the number of patients that can be accepted in the event of changes in the number of nursing personnel.

Literature Review
Te medical industry is a labor-intensive service sector; thus, HRP is essential in this industry. In general, approximately 30% of the personnel in an acute hospital are nursing staf members. Nurses thus constitute the main personnel in hospital operations. In modern medical treatment procedures, nurses must provide highly professional care to patients. A lack of sufcient nursing staf for posttreatment care might lead to high risks of patient relapse. Tus, nursing staf members play crucial roles at every level in medical institutions.
In general, a higher ratio of nursing staf to patients is associated with superior patient recovery [7,8]. However, nursing jobs are highly exhausting, and nursing staf must spend considerable time interacting with and satisfying the demands of patients or their families; these requirements impose a high burden on nursing staf members. Consequently, medical institutions experience a high turnover of nursing staf [9]. According to Waldman et al. [10], Most of the hospital stafs are nursing personnel; therefore, the turnover cost for nursing personnel accounts for approximately thirty percent of the total turnover cost. A study indicated that more than 20% of the nursing staf in hospitals had the intention of quitting their job each year in general [11]. A shortage of nursing staf can considerably increase patient mortality rates [12,13] and in-hospital infection rates [14]. Moreover, a lack of adequate nursing staf might lead to insufcient preservice training and evaluation skills, which result in communication disruptions and thus medical adverse events, including falls [15], medication or transfusion errors [16], treatment delays, complications during or after surgery [11,17], and prolonged hospital stays [11].
According to Chiu et al. [18], the cost of training a new registered nurse is US$15,825 in the U.S. In addition, insufcient nursing experience results in productivity reduction, the estimated cost of which is US$5,245-US$16,102; it also engenders medical adverse events, which are also associated with a high implicit cost. Terefore, planning strategies for hiring nursing personnel constitute a crucial component of the overall labor planning process of hospitals. Te insufciency of nursing staf is a problem faced by hospitals worldwide [18].
Hospital managers must develop suitable incentives to increase nursing staf retention. However, if managers adopt only salary hikes as a strategy for nursing staf retention, their hospitals would experience high operational pressure because their expenses would increase while their income would remain limited by health insurance systems. Failure to address the problem of nursing staf turnover might lead to a deterioration in nursing quality, which would lead to patients providing poor reviews regarding the hospital. Poor reviews can result in a sharp decrease in hospital income. In Taiwan's insurance payment system, nursing expenses are included in hospital expenses. Te salary covered by this system for each nursing personnel is less than $20,000. Tus, hospitals can reduce their nursing expenses only by reducing the number of nursing staf employed [19], hiring contracted staf instead of employees, adopting a working-hour-based salary system, and not recruiting new staf even when vacancies exist. Decreases in the ratio of nursing staf to patients result in staf demoralization and thus high turnover rates. Terefore, hospitals should employ a suitable number of nursing staf such that they minimize expenses while maintaining high health-care quality.
HR quality is more important than HR quantity in most of the industries [20], including the medical industry. Health-care staf members typically difer in terms of literacy, health-care capability, and service quality. Terefore, "clinical advancement systems" have been developed in the nursing industry. Continual on-the-job training can help nursing staf to improve their nursing skills, knowledge, and self-growth, thus increasing their service quality. Te current clinical advancement system in Taiwan is based on Benner's theoretical structure, which comprises fve stages of skill acquisition in nursing knowledge: novice, advanced beginner, competent, profcient, and expert. Te purposes of this system are to help nursing staf transform from novices to experts through step-by-step learning [21,22] and to reduce staf turnover by higher job achievement.
Managing turnover is crucial for frms because retaining the best talents is essential to remain competitive in the 21st century. Many HR managers have termed the current era as the era of the war for talent [23]. To address the problem of turnover, numerous studies have attempted to determine the key factors that drive turnover [24][25][26][27]. However, healthcare staf turnover is a dynamic problem because the interrelationships between the factors that infuence it to vary. Furthermore, the assumptions underpinning the models constructed in previous studies for assessing health-care staf turnover might become invalid over time. Tis can thus engender uncertainties regarding the impact of strategies suggested by such models. Consequently, organizations face high risk in strategy implementation, especially when the implemented strategies are inefective. Considering these limitations, static decision-making models might be unsuitable for modeling health-care staf turnover because they cannot integrate all the variables of a real situation. Te basic assumptions of decision-making models are that criteria and alternatives are fxed a priori and that a decision occurs only once; that is, a decision does not involve spatial or temporal considerations. Tese assumptions limit the validity of the results of the aforementioned models, especially when parameter values change over time and the decision matrix is not fxed or static. In addition, multicriteria decision-making models for talent retention policy selection focus on the cause-efect relationships between individual factors; hence, these models are not comprehensive. Multicriteria decision-making models also generally cannot provide a complete understanding of the complexity of the problem of talent retention policy selection with respect to human-related factors.
Forrester identifed a defciency in the decision-making process of complex dynamic systems [28]. To overcome this defciency, he proposed SD modeling tools that allow the refning and simulation of mental models for diferent decision-making policies. Studies have applied SD to address several management problems and provide decision support for managers in many felds [29][30][31][32]. A suitable decisionmaking model must be able to tolerate vagueness or ambiguity because fuzziness and vagueness are common characteristics of most decision-making problems [33]. Accordingly, fuzzy logic (FL) is an essential way for an efective decision-making model [34][35][36][37]. Te fuzzy theory is the most commonly used concept for solving problems related to imprecise data and ambiguous human judgments in the selection of a talent retention policy. Fuzzy set theory was created to adapt mathematical tools of logic to diferent types of uncertainty, such as vagueness and approximation, which are characteristics of natural language and human mental models. FL enables the representation of human knowledge through linguistic IF-THEN expressions, which are typical of approximate reasoning [38]. Moreover, FL can be used to obtain solutions to many real-world problems that involve some degree of imprecision and ambiguity, such as talent retention policy selection. Data shortage, measurement errors, or the subjectivity of human judgment can result in uncertain information exhibiting a fuzzy or stochastic nature. Fuzzy models are commonly used because they address various types of uncertainties.
Hybrid models combine diferent forecasting methods to estimate policy performance. Te main advantage of these models is that they can combine diferent methods and thus leverage their advantages; nevertheless, verifying the rationality of the approach used to combine such methods is difcult. Moreover, hybrid models are characterized by a long computational time.
Te frst researchers to integrate FL and SD were Pankaj et al. [39], who proposed a method for the qualitative analysis of causal loops by using fuzzy linguistic uncertainties to incorporate the perceptions and beliefs of the modeler. Teir motivation was based on the understanding that natural language is the optimal means of expressing the relationships between variables in human mental models. Tis perception is also the reason behind the development of Journal of Healthcare Engineering 3 most hybrid models. Several studies have integrated FL into SD models so that they could consider fuzzy parameters (i.e., their relations, arithmetic, or soft descriptions) when data are unavailable or are not sufciently credible or when certain parameters exhibit fuzziness [40][41][42]; these studies did not use FL to defne policies to control the developed SD models but instead used it to handle the uncertainty in some model parameters. Tese models were controlled through a classic approach entailing the use of crisp parameters. Song et al. [43] and Orji and Wei [44] have used SD models to simulate alternative scenarios and then ranked them through MOP. Similarly, Chang and Ko [45], Xu et al. [46], and Wu and Xu [47] have used MOP to control each step of an SD model. Tis approach is similar to the methodology proposed in this study in that the controller is completely dissociated from the model to be controlled in both approaches. Sabounchi et al. [48] used FL to model decision rules in an SD model of users' transportation preferences.
On the basis of the preceding literature on the combination of FL with SD, we can determine that no study has combined FL with SD modeling for the selection of talent retention policies. Accordingly, the main aim of this study was to design a multiobjective FL-based SD method to handle constraints and uncertain parameters in the evaluation of talent retention policies.

Methodology
Te SD approach is based on systems thinking and is aimed at facilitating learning tasks in complex, feedback, multiloop, multistate, and nonlinear systems in which humans live [49]. It involves using systematic thinking tools to modify mental models repeatedly for implementing refective learning. Sterman [50] suggested that the SD approach is the best method for resolving complex and dynamic problems. An SD model that considers the interrelationships between internal and external factors can provide specifc information related to a complex and dynamic problem and then provide suggestions for the perfect strategic decisions for solving the problem, which would be helpful for managers. In this study, we used the general modeling method proposed by Forrest [51]. SD models are designed to determine the structure of a complex system through the comprehension of concepts such as feedback, stocks, fows, time delays, and nonlinearity [52]. Te major components of an SD model include stocks, fows, rates, and auxiliar. Time delay is the most crucial factor in an SD model.

Case Study and Problem Specifcations.
We conducted a case study on a private and not-for-proft metropolitan hospital in the North of Taiwan. Although this hospital is not a medical center, it is the largest institution with the most beds in the area it is located. Te hospital adopts a performance-oriented administrative culture. Various performance management systems have been implemented in this hospital for various posts. Consequently, this hospital is far ahead of the other hospitals in the area in terms of fnancial performance in the health insurance application. However, the hospital is located in a remote area; thus, it encounters difculties in retaining personnel. Problems related to HR outfow exist for all the positions in the hospital. Although each hospital employee signs a contract when accepting their job ofer, they usually choose to leave the job when their contract expires. Despite improvements in the transportation infrastructure that have removed geographic constraints between the rural area in which the hospital is located and the nearby urban area, employees who remain with the hospital after their contract period are usually locals. In addition, the hospital is a leader in the medical industry; thus, to compete with hospitals in urban areas in attracting talents, it has raised the salaries of its employees, which has led to an increase in its operational costs. Consequently, the net profts of the hospital have decreased within a very short period. However, the hospital still has been unable to solve the problem of HR outfow. Other hospitals that are located in the same area and are of the same level as the case hospital are mostly public institutions or associated with a religious organization, and they have a strong focus on services (e.g., integrated delivery system). Employees of these other hospitals work there because they share altruistic ideals. Tus, these other hospitals need not increase the salaries of their personnel to remain competitive with hospitals located in urban areas. Te national health insurance (NHI) system in Taiwan has been adjusted to the managed care-related related policy in recent 20 years. Hospital income cannot be increased without limitation; however, HR costs are still very high.
In this study, the SD modeling process involved fve essential steps [53]: (a) problem articulation (boundary selection), (b) dynamic hypothesis formulation, (c) simulation model creation, (d) testing, and (e) policy design and evaluation. Te information used for the study was collected from archival records and interviews with health-care personnel, namely, fve health-care managers and two directors in the nursing department of the case hospital. Moreover, fve strategies were considered as alternative talent retention policies for assessment.

Causal Loop
Diagram. Te frst step in developing an SD model is to defne a causal loop diagram. Causal loop diagrams are useful for identifying the feedback loops involved in a process and for representing the feedback structures of systems. Te developed SD model captures the relationships between all nodes, including patients, medical staf, hospitals, hospitals' HR policies, and total hospital expenses, to defne the system boundary. In this study, the causal loop diagram for the problem of talent retention policy selection focused on nursing staf duty, work pressure, and external information disclosure criteria.
Te causal loop diagram described the fve aforementioned talent retention policies with respect to the three criteria (nursing staf duty, work pressure, and information disclosure criteria). Te developed SD model assumes that when the hospital recruits a new staf member, the workload in the team increases, resulting in this or other staf members resigning and leaving the system; this represents a sequential process, with the new staf member being the frst point (stock) of the sequence. Te rate of stock infow was determined. Tis study set the system boundary on the basis of relevant internal factors, including the number of patients and care staf members; external factors, including population served by the hospital, number of other competing hospitals, insurance budget, and hospital administration policy. Te problem specifcation and the causality of the overall system are described as follows.
Most medical utilization models consider the mutations of epidemic diseases and special health check-ups, but these items are not covered by insurance systems. Medical staf members experience work-related stress when their hospitals adopt new technologies that are challenging to operate. Tus, medical institutions must frequently retrain their staf members to improve their health-care provision skills, which can reduce their work-related stress. Moreover, new employees increase the burden and stress exerted on existing employees because they are unfamiliar with their job processes; the high proportion of new employees (with 30% of front-line stafs of the hospitals being new employees) can be attributed to the high turnover rate of health-care personnel. Because of the burden and stress induced by new employees, staf morale is relatively low, and the health-care quality decreases; this leads to the resignation of existing personnel, thereby creating a vicious circle. A decrease in health-care personnel leads to a decrease in health-care supply and an increase in the duty ratio (health-care demand/health-care supply), which imposes extra stress on front-line personnel and leads to a further increase in their turnover rate. Te expansion limits set for hospitals by the health-care insurance organization when preparing its budget are based on regional totals and the calculation method of point values. Hospitals frequently adopt incentive measures to increase their market share, and these measures often increase their medical resource consumption and expenses. Moreover, the performance system causes increases in the number of patients and the personnel workload. Medical institutions require a prolonged time to recruit new employees in response to increases in workload. Failure to promptly recruit new employees to take up the excess workload leads to stress among existing personnel, and this ultimately increases their turnover rates; the high turnover increases the institution's expenses. In summary, factors such as population aging lead to an increase in the demand for medical services; nevertheless, the supply of such services is limited and is governed by the total number of people paying insurance premiums. Tus, relevant authorities have developed many policies to restrain the growth of hospitals' expenses and reduce their expenses if possible. However, as displayed in the causal loop diagram, a reduction in hospital expenses might increase health-care risks. When insufcient health-care personnel is available to meet patients' health-care demands, some balancing policies must be adopted to ensure that patients' rights and treatments are not negatively afected.
To estimate the performance of diferent strategies for workload reduction, factors related to revenue sustainability, such as the total insurance budget/cost associated with a particular nursing staf member, should be considered frst.
Te performance of diferent strategies was estimated by experts by using fuzzy questionnaires and real data collected from the case hospital. Te following fve HR balancing strategies were evaluated in this study [6].

Policy 1:
Changing the Care Model. Policy 1 involves replacing the original primary nursing model with a functional care model. However, although the adoption of the functional care model can temporarily increase efciency, the root problem of insufcient medical supply still exists. Tus, personnel are still under stress and may eventually resign. Policy 1 might help balance the causal loop over the short term; however, it can also lead to a long-term time delay efect. Terefore, policy 1 has unsuitable efects over the long term.

Policy 2:
Increasing Working Hours. Policy 2 involves making health-care personnel work overtime. Te number of patients and the workload of long-term care institutions are somewhat fxed, and employees often work overtime in these institutions. However, health care is a persistent job. Te tasks involved in each shift must be handed over to the person working the next shift, and many varied tasks are conducted in hospitals. In the short term, increasing working hours can increase the medical supply; however, over the long term, overtime might lead to high turnover rates and thus a time delay efect.

Policy 3: Increasing the Number of Patients Attended to by Each
Health-Care Professional. Patients must be cared for even when the supply of manpower is insufcient. Patients cannot be discharged because of an inadequate workforce. Terefore, the number of patients assigned to a single healthcare personnel is increased to meet care needs. When the number of health-care employees in a hospital decreases, the duty rates for the remaining employees are increased because the number of patients is unchanged. According to the literature, when the number of patients to be cared for by each health-care professional decreases by 1, the corresponding health-care quality, staf morale, and job satisfaction decrease [12,14], which results in personnel resignations over the long term. Tus, policy 3 results in a time delay efect over the long term.

Policy 4: Increasing the Number of Care Staf Members.
Although an upper bound exists for the number of patients assigned to each health-care personnel (i.e., a maximum of 2.5 beds assigned to a single health-care personnel), hospitals usually consider their entire staf, including those in administrative units, outpatient units, and other special units, when evaluating the number of patients to assign to their personnel. Tus, the actual number of available personnel is diferent from the reported number of personnel. Consequently, when the number of care personnel decreases, the workload of the remaining personnel increases considerably. Because the HR departments of hospitals consider only the total number of personnel as a basis for recruitment, the Journal of Healthcare Engineering number of care personnel hired might be insufcient, which negatively afects the provided health care and increases the workload of health-care personnel. Tis also engenders a time delay efect.

Policy 5: Reducing the Number of Available Beds.
Under policy 5, the numbers of beds and health-care personnel are regulated according to the ratio of beds to total personnel. When the number of personnel is insufcient, some wards can be closed or the bed availability can be reduced. Te removal of beds results in a decrease in longterm medical demand. However, this measure does not help reduce the immediate medical demand or the number of person-days of hospitalization. Consequently, the workload might increase in the short term. Te main problem associated with removing beds is that hospitals cannot turn away patients, and reducing the number of beds would result in complaints about long waiting periods for hospitalization. Tus, the stress on employees might increase over the long term, which is a time delay efect.
On the basis of the preceding analysis, this study established a diagram to demonstrate the possible reason for the high turnover of health-care staf (especially nursing staf) and to outline policies that can be adopted by healthcare institutions to address the problems caused by the high turnover, as presented in Figure 1. Te next section presents the stock and fow diagrams as well as their equations, all of which were used to analyze the relationship of the policies and the stabilize of the HR structure in the case hospital. We attempted to identify a suitable strategy for handling care staf turnover.

Stock Flow Diagram
. Te proposed SD model combines HR demand and HR supply to evaluate HR policies. On the basis of the aforementioned causal loop diagram, we created a stock-fow diagram. Subsequently, the dynamic equations for each element in the stock fow diagram were added to the developed SD model.
Te ultimate purpose of an SD model is to help a manager simulate the infuences of management decisions on system growth and stability in a management system. Te manager can then develop measures or policies to improve system performance. Terefore, only the manager can decide whether the SD model helps improve the actual management performance.
In the proposed methodology, the system to be governed (modeled using SD stock and fow language) is separated from the human decision-making system (policies). A stock node (symbolized by a rectangle) represents a point where content can accumulate and deplete. A fow node (symbolized by a valve) is a rate of change in a stock node, and it represents an activity, which flls in or drains the stock node. An auxiliary node or a constant node can store an equation or a constant. Finally, the connectors, represented by simple arrows, are the information links representing the cause and efects within the model structure; the double arrows represent physical fows. Double lines across the arrows indicate time-delayed information.
We created our stock fow diagram for the health-care subsector by using the number of care staf members and the workload information. Providing health care to patients is a skill. Te experience of health-care personnel infuences the quality of the care they provide and their risks of making errors during care provision. According to the HRP model proposed by Nkomo, experience diferences between personnel should be considered to reduce errors in evaluations. Terefore, the present study referenced the skill acquisition model developed by Hubert and Dreyfus to design an HR classifcation structure [54]. However, interviews with administrators from the case hospital indicated that the developed fve-level structure was excessively complex. Terefore, we categorized nurses in the second year of their job as advanced nurses, those in the third year of their job as senior nurses, and those holding a position in the administration or nursing department as experts. Te stock-fow diagram for HRs in nursing is displayed in Figure 2.
Te trial period for each employee in the case hospital is 3 months, and those who pass their trial period become ofcial employees. New recruits are junior nurses, who become senior nurses after gaining 1 year of experience. Every year, the case hospital conducts a survey of employees' willingness to remain at the hospital. Tose who wish to resign can be classifed into the category of "expected to leave ofce." According to the manager of the case hospital, personnel changes after the expiry of contracts are usually related to transfers from a frst-line post to another post or resignations due to family needs. As revealed by annual survey data, the turnover rates of the case hospital are 65% and 30% for advanced and senior personnel, respectively.

Calculating Number of Care Staf Members and
Workload. To determine HR supply and HR demand, the current number of staf members must be calculated. Moreover, weights should be assigned for various factors for calculation. According to the interviews conducted in this study, the case hospital adjusts its number of job vacancies on the basis of its current HRs. Te main recruitment stages are usually implemented after two national exams every year; however, the number of people the hospital has recruited and the number of people it reports to have recruited are two factors that should be considered for calculation. In addition to the workload demand, the number of people of diferent seniority levels leaving the hospital should be considered during the calculation of the quantity of resources required to fll these vacancies. Te time required to fnd suitable candidates usually difers for diferent seniority levels. An interviewee stated that fnding suitable candidates immediately was impossible. Terefore, in the case of departures, the additional workload was spread among the remaining personnel. Consequently, the weight pertaining to workload could be set to 1.
Because the seniority of frst-line health-care personnel might infuence their service quality, a suitable weight should be adopted for personnel at each seniority level. Terefore, we set a weight of 1 for senior staf and experts. Te interviews also indicated that during the trial period, personnel usually spend their time learning. Moreover, they provide care to patients with simple conditions. After the trial period, personnel are fully integrated into the healthcare provision system. Senior staf must spend time teaching new staf in the trial period. Accordingly, we set a weight of −1 for senior staf providing assistance during the trial period. Moreover, directors cannot engage in health care when they are interviewing junior staf. Terefore, we set a weight of 0.8 for directors. Finally, we set a weight of 0.9 for registered nurses who plan to leave the job after the expiration of their contracts. Because the weight of the resignation possibility includes negative numbers, we adopted a setting to avoid negative values.
A higher person-days of hospitalization might lead to higher workloads for health-care staf. However, for calculation, an assumption of a three-shift system (day, evening, and overnight shifts) would be more convenient than a 24 hours way; thus, person-days were converted into hours. Te maximum number of patients assigned to each care personnel in the three-shift system was set to 8, 10, and 12 for the day, evening, and overnight shifts, respectively. Moreover, the time required for patient care varies with disease severity. Hence, we also considered disease severity in terms of the Carlson comorbidity index and set the risk ratio to 1.2 [55]. We also set the daily nursing hours to 8 h per day. Because working overtime is highly common in hospitals, a corresponding parameter was added to the system dynamic model.
Health-care workloads might increase because of changes in health-care tasks, and increased workload is a Journal of Healthcare Engineering major reason for HR outfow. Tis time delay factor should be considered before applying any response measures. Tus, the nursing workload ratio was set to 1. A nursing workload ratio higher than 1 indicates excessive workload. Te time required to recruit new staf to fll vacancies was set to 6 months. Because the provided health care afects people's health considerably, medical service quality must be considered when assigning jobs. In addition, upper bounds should be set for the workload. Accordingly, the upper bound was set to 12, 15, and 18 patients for the day, evening, and overnight shifts, respectively. Te literature reveals that a positive relationship exists between work pressure and HR outfow. Tis study thus developed an HR outfow function ( Figure 3) and a stock-fow diagram (Figure 4) for the analysis of staf workload.
In general, if a manager wishes to make a suitable policy decision, they must consider strategic approaches toward multiple policy objectives. Moreover, they should avoid linear thinking to avoid making wrong decisions. However, determining the best multiobjective policy through humans' limited thinking loops is difcult. Terefore, the MOP model can be used to design diferent objective functions under a set of constraints for decision-making in systems involving two or more goals.
As mentioned, every system has unique objectives and requirements pertaining to workforce planning. To achieve all objectives and fnd the best solution, all the adopted systems must be balanced in every loop. Patients generally wish to receive the best (most expensive) service; however, the insurance expense system of a hospital must minimize the hospital's claimed expenses. Terefore, a hospital management system is typically designed to increase the hospital's revenue by maximizing its income and minimizing its costs (the labor cost accounts for the highest percentage of all costs in a hospital). Employees prefer their labor payment to be increased to the highest amount possible. If the labor payment is insufcient, employees' willingness to ofer high-quality services might be infuenced, which can considerably infuence patients' perceptions of the hospital. Tus, optimizing the aforementioned multiobjective parameters through SD modeling can facilitate a more comprehensive policy consideration process. We conducted simulations for the multiobjective optimization model developed in this study by adding insurance and workforce constraints to the model. We also considered the efects of turnover on the balance of possible institutional changes or structural workforce changes. Tese efects were determined by decision nodes, which were represented by the growth rate of each industry, in the simulations. Some of the constraints used in the baseline scenario are described as follows.
(1) Population Subsystem. A strong relationship exists between medical demands and population. We defned the demand subsector and population subsector. Population data obtained from the Department of Statistics, Ministry of the Interior, Taiwan, revealed that by the end of 2013, a total of 458,456 people resided in the county in which the case hospital is located. Among them, 88,112 people (20% of the county population) were aged older than 65 years. Overall, elderly people constitute 11.53% of the population of Taiwan in 2013. Terefore, the aforementioned county has a high population of elderly people. Table 1 presents the population trend over the past 10 years in this county. Population aging engenders increased medical demand and increased workload for health-care staf.
(2) Revenue Subsystem. Te Taiwan NHI system is diferent from those of other countries with a family doctor system. In Taiwan, no appointment system exists for outpatient services; however, moral constraints prevent doctors from declining any patient. Most Taiwanese hospitals have a culture of performance incentives based on physician fees. Terefore, the numbers of patients in Taiwanese hospitals are very high, which leads to high workloads and work pressure for health-care staf. Accordingly, we collected data on the monthly numbers of patients in the case hospital to defne our simulation parameters. With regard to medical revenue, the data collected by this study from the case hospital included medical income from inpatient and outpatient services covered by the NHI program, medical income from medical services paid by patients, and nonmedical income. Te main revenue source of the case hospital was the income obtained from services covered by the NHI program; information regarding all other sources of revenue was confdential. Terefore, our simulations were related to the services covered by the NHI in the case hospital. Partial revenue data for the case hospital are presented in Table 2.
(3) Care Provider Subsystem. Te purpose of this study was to analyze the infuences of the HRP policies of a medical institution on the outfow of its health-care staf. Tus, the HR supply data used in this study comprised the number of nursing personnel in the case hospital and the number of personnel resigning from the case hospital. We collected monthly data regarding the experience levels of the nursing staf (N-N4) and the number of personnel of each  Journal of Healthcare Engineering level who resigned from the hospital (including those who resigned and those who could not perform frst-line tasks because of diferent reasons) over a 5-year period. In general, the peak period for nursing staf outfow in the case hospital was determined to be from July to September and from February to April. Table 3 presents a summary of the number of nursing staf members who resigned from the case hospital over the 5-year period, which increased exponentially.

Fuzzy MOP
Model. An MOP model is typically used to maximize or minimize diferent objective functions under a set of constraints and is essential for decision-making in systems involving two or more goals. In a system for selecting a suitable strategy for health-care talent retention, each subsystem has unique goals, and each item must be optimized to achieve a suitable trade-of among the subsystems. In general, in such a system, the health-care institution's revenue and insurance revenue must be maximized, whereas the HR cost must be minimized. To achieve these goals, system parameters that strongly infuence the system output must be identifed. Accordingly, we developed an MOP model and applied it to a dynamic system to optimize its parameters. Te notations used in this section are listed in Table 4.     Objective related to a health-care institution's revenue f 3 Objective related to human resource planning G 2 Patient care revenues E1 Revenue of hospital E3 Revenue of district hospital x 1 Growth rate of hospital x 3 Growth rate of hospital x 5 Proportion of investment in the remaining staf C 1 Global budget for western medicine consumption C 3 Global budget for dental medicine consumption C 5 Reduction in hospital expenses after the implementation of the global budget s i Consumption coefcient of fee i to human resource loss α 1 Restrictive impact factor coefcient for the global budget system f 2 Objective related to the insurance system G 1 Patient care revenue under health insurance G 3 Nonpatient revenue E2 Revenue of a metropolitan hospital E4 Revenue of a clinic x 2 Growth rate of a metropolitan hospital x 4 Administration fee in the global budget C 2 Global budget of western primary medicine consumption C 4 Global budget of Chinese medicine consumption a i Te exhausted of care staf equivalent transformation coefcient of the insurance of fee i e ij Consumption coefcient of fee i per unit of output for the jth hospital level α 2 Implement impact factor on coefcient of human loss policy 10 Journal of Healthcare Engineering

Objective Function (1) Objective Related to a Health-Care Institution's Revenue.
Health-care institutions are nonproft organizations; however, they must generate sufcient revenue to operate sustainably. Some health-care institutions have also started commercializing their services. Tey must earn revenue that at least equals the operating cost and the capitalized cost related to the new investments. In addition, under the infuences of an unlimited insurance policy and private patient fees, achieving maximum revenue has become a major objective of most health-care institutions. Tis objective can be considered the frst objective in this study and can be expressed as follows: (2) Objective Related to the Insurance System. Unlimited growth in the global insurance budget is impossible, and this budget infuences the economy and civil atmosphere of a nation. Rapid aging in a society engenders increased healthcare demand, and a gap between health-care demand and supply is a developmental bottleneck for health-care institutions. Terefore, reducing insurance fees is a major objective of the National Health Insurance Administration (NHIA) of Taiwan, which can be considered the second objective in this study. Tis objective can be expressed as follows: where C 1 , C 2 , C 3 , and C 4 represent the global budgets of western medicine consumption, western primary medicine consumption, Chinese medicine consumption, and dental medicine consumption, respectively, at the three hospital levels (medical centers, metropolitan hospitals, and district hospital). Moreover, C 5 denotes the insurance amount saved through any budget control policy.
(3) Objective Related to the HR Cost. Te expansion of a hospital is limited by the total population in its region and the global budget of insurance fee point calculation systems, which can result in a crowding-out efect. Tus, hospital expenses should be decreased to raise hospital profts; the HR cost accounts for the highest proportion of the total expenses of a health-care institution. However, according to the causal loop diagram, expense reductions might increase the risks associated with patient care. Terefore, the HR cost must be minimized such that patient safety is not compromised. Tis can be considered the third objective in this study and can be expressed as follows: Te fnal item in equation (3) is the NHI claim reduction resulting from the health-care institution's internal adjustment policy.

Constraints.
Decision-makers select their preferences for the relationships between factors or variables in an HRP system, and these preferences are then considered as constraints for MOP.
(1) Constraint Related to the Growth of a Health-Care Institution. Health-care demands and expenses increase with the growth of the elderly population in an area. However, increases in the use of insurance resources and institution costs must be limited while meeting the health-care demand. Terefore, an upper bound for the growth rate of a healthcare institution is a constraint in an HRP system. Moreover, the growth rate of NHI fees must be higher than the development rate of health-care institutions in the relevant country. Accordingly, the constraint for the growth of a health-care institution can be expressed as follows: where d 1 represents the minimum growth rate of insurance fees.
(2) Investment Constraints. Most health-care institutions in Taiwan are nonproft organizations covered by insurance, which indicates that they have limited income. Tey cannot invest in other businesses and must use their revenue for their own needs. In general, the manager of a health-care institution must strive to achieve a cost allocation of 33% for each of the following aspects of their institution: HRs, medicines, and utilities. Terefore, the proportion of investment into HRP is limited. Let d 2 and d 3 represent the upper limits of the global budget and HRP budget, respectively; hence, the following equations can be derived: (3) Insurance Source Constraints. Insurance consumption mainly varies with the age of, health-care literacy of, and medical advice obtained by an individual. Moreover, the density of hospitals in an area and the proportion of the population seeking medical advice in this area govern the consumption of insurance resources, especially after the implementation of the capitation and fee-for-service reimbursement system. To control the growth rate of insurance consumption, the NHIA can set fxed thresholds or constraints to regulate the frequency at which people can seek medical advice and the frequency of hospitalization (e.g., global budget or diagnosis-related group system). Accordingly, the following proportional constraints can generally be applied: Moreover, the insurance budget for the current year should be less than that for the previous year. Hence, the following inequality should be satisfed: where IF denotes the insurance fee for the previous year and d 4 is the average rate of increase in this fee.
(4) Constraint Related to the HR Cost. Te HR cost generally accounts for the highest proportion of the total cost incurred by a health-care institution. Terefore, from an administrator's viewpoint, an increase in HR costs should be minimized. Te constraint for the increase in HR cost is similar to that for the increase in insurance resource consumption, and the following inequality should be satisfed: where HC denotes the HR cost in the previous year and d 5 denotes the average rate of increase in this cost. On the basis of the aforementioned analysis, the established multiobjective model can be expressed as follows:

Fuzzy Extensions.
In a multiobjective model, many coefcients and parameters must be determined. Some of these parameters can be obtained from historical records such as local statistical records. For parameters with inadequate, incomplete, imprecise, or inconsistent data, domain experts can subjectively determine the values for these parameters. Because HRP involves uncertainties and great infuence, each considered HR policy in this study could not be implemented realistically in the case institution. As mentioned, fuzzy programming is useful for solving programming problems involving uncertainties. Accordingly, this study incorporated fuzzy programming into the aforementioned multiobjective model to handle potential uncertainties in the selection of health-carerelated HRP. In general, the triangular fuzzy parameters, which can be expressed in terms of a triplet of crisp numbers [i.e., (r 1 , r 2 , r 3 , where r 1 < r 2 < r 3 ], are used to describe fuzzy coefcients. Te membership function of a fuzzy parameter can be expressed as follows: Fuzzy parameters are assumed to be triangular; therefore, the fuzzy equivalent of a can be denoted as ã. Let be x a decision vector; ξ be a fuzzy vector; f i (x, ξ), i � 1, 2, . . ., n, be an objective function; and g i (x, ξ) be a constraint function. Terefore, the following equation can be obtained for a fuzzy multiobjective decision model: Tis model can be used to solve fuzzy programming problems. Because of this model's fuzzy nature, its precision cannot be compared with that of a mathematical model. Domain experts must thus determine the expected values of the model parameters. For the triangular fuzzy parameter ã � (r 1 , r 2 , r 3 ), the expected value is ã � 1/3 × (r 1 + r 2 + r 3 ). By calculating the expected values for fuzzy parameters, experts can transform a fuzzy multiobjective model into a classic crisp MOP model, whose solution can be derived using the method described in the following section.

Method for Solving Multiobjective Problems.
In general, four types of methods are used to solve multiobjective problems: methods with no articulation of preference information, methods with a priori articulation of preference information, methods with a progressive articulation of preference information, and methods with a posteriori articulation of preference information. Solving a multiobjective problem basically involves transforming it into a single-objective problem. Te most common approach for this transformation is the weighted-sum method, which involves a posteriori articulation of preferences. To illustrate the weighted-sum method, the following multiobjective problem can be used as an example: Te frst step in the weighted-sum method involves solving the following functions: max f i (x)s.t., x ∈ X and min f i (x)s.t., x ∈ X, where i � 1, 2, . . . . . . n. Tese functions are solved to obtain the optimal value for each singleobjective problem.
Te second step entails applying the optimal values obtained in the frst step to defne new functions as follows: Te third step involves transforming the original problem into a single-objective problem as follows: where w i is the relative weight of the ith objective such that w i ≥ 0, n i�1 w i � 1. Te solution to the problem expressed in the preceding equation is a Pareto-optimal solution, which is satisfactory for the original problem. By using the weighted-sum method, a decision-maker can easily adjust the importance of each objective. Consider, for example, the three objectives outlined in Section 3.6.1. Te parameters w 1 , w 2 , w 3 , w 4 , and w 5 denote the relative weights of the objectives pertaining to health-care institution development, the patient health system, the insurance spending system, the staf assignment system, and care risk management, respectively. If the importance of the health-care institution's development must be emphasized, w 1 can be set to 0.6 and w 2 -w 5 can be set to 0.1. However, if all fve objectives are considered to be of equal importance, w 1 -w 5 are set as 1/5.

Model
Test. According to Coyle [56], the validity of an SD model does not depend on its absolute accuracy; instead, it depends on its suitability for solving the complex and nonlinear problems. Forrester [28] also stated that an SD model developed for a complex high-order nonlinear system with numerous nodes cannot be validated using general statistical methods. Tese statements are valid because SD models refect real-world situations. If some nonsignifcant node relationships in an SD model are removed, the purpose of developing the model might not be achieved [49]. Considering these statements, we adopted Sterman's [49] suggestion and performed a model behavior test and model structure tests. Te following model structure tests were performed using the Vensim 6.3 DSS simulation software tool: structure verifcation, dimensional consistency, and extreme condition tests.
In the structure verifcation test, we performed two interviews: one before the causal loop diagram was created and one after the fow diagram was created. By exploring the case hospital's management problems, we determined the main simulation structure required for conducting policy simulations in this study. After identifying and confrming the relationships, we performed syntax checking, singleequation checking, lookup usage checking, model checking, and multiple-equation checking by using functions of the Vensim software.
In the dimensional consistency test, we mainly evaluated whether clear and reasonable constants and node values could be calculated by unit synonyms and unit-checking tools to avoid inconsistent unit problems. Te simulations conducted in this study were based on real data obtained from the case hospital; therefore, month, which is often used as the unit in models developed for selecting general human afairs strategies, was adopted as the basic unit of the developed SD model. Te unit of all the nodes was set to month for consistency. Before starting the simulation procedure, we used the Vensim unit checking tool to ensure that all parameter units were consistent. Te formulae and parameters are listed in Table 5. In the extreme condition test, we used two conditions to confrm whether the adopted simulation structure was correct. In the frst method, the insurance income was set to 0 when the population was 0. In the second method, the care demand was set to 0 when the occupancy rate was 0.
In the model behavior test, diferent sets of data were used for diferent purposes. Tis test was used to determine whether the simulation results matched the real data from the case hospital. We attempted to determine whether the workload ratio and HR outfow would increase with the occupancy rate. All the simulation results were as expected and exhibited a trend of exponential growth.

Simulation and Results
Simulations for the designed system were conducted using the developed SD model. Te model parameters were determined from hospital data provided by the Ministry of Health and Welfare in Taiwan, open data provided by the Taiwanese government, and information provided by the case hospital. Baseline scenarios were designed on the basis of the real revenue and nurse-patient ratios of the case hospital. We performed microcosm and macrocosm simulations in this study.

Policy Simulation Results Obtained with a Microcosm
Model for the Case Hospital. Te microcosm efects of diferent HR policies on the case hospital were analyzed using fve practical conditions. Regarding HR outfow, primary-level health-care personnel often suggest that the standard patient-nurse ratio should be reduced. Specifcally, they suggest that the number of patients requiring care should be decreased to reduce their heavy workload, which can mitigate the problem of HR outfow. Accordingly, we frst simulated the efects of reducing the aforementioned ratio in the case hospital. We considered the three nursing models that are currently adopted in hospitals: primary nursing, team nursing, and functional nursing. Primary nursing is currently the most commonly used nursing model. In this model, one nurse must take care of several patients. Nurses only make plans for their patients and complete their tasks during their working hours (in this study, we assumed that three shifts exist per day and reduced the patient-nurse ratio for evaluation). Team nursing involves a group of nurses taking care of a group of patients. Diferent groups of patients are taken care of by nurses with diferent levels of experience. Job arrangements for nurses in the same group are based on their experience. We considered nurses of diferent levels, divided them into four groups, and performed a simulation using the same number of patients for the groups. Functional nursing is a taskcentered nursing model that involves assigning specifc tasks to personnel. Because some studies have indicated that the efciency of the functional nursing model is high, we selected seven main tasks: material management, medication (injection), nursing planning, temperature, pulse, and respiration (TPR) measurement, making beds, training, and caring, as the basis for our calculations. We performed the simulation by increasing the quantity of HRs by 1.2.
Te simulation results obtained for the nursing model and patient-nurse ratio are displayed in Figure 5. Te care workload ratio did not decrease considerably when the patient-nurse ratio was reduced or when the functional nursing model was used. However, when the team nursing model was used, the care workload ratio was efectively reduced. Tese results indicate that reducing the standard patient-nurse ratio did not efectively reduce the care workload ratio. Instead, it led to uncertainty in the number of available beds, which increased administrative costs. When nurses with diferent experience levels work in groups, the pressure imposed on them decreases, which consequently reduces the personnel turnover rate.
In the second simulation, we increased the level of overtime, and the results are shown in Figure 6. An increase in overtime initially caused a decrease in workload. Nevertheless, the workload subsequently increased to the original level with time. Tus, the aforementioned policy was not helpful in reducing HR outfow.
In the third simulation, we adjusted the levels of experience of the nurses to increase the health-care efciency and number of patients cared for. We simulated the efects of applying diferent policies, such as incentives, retention bonuses, and high salaries, for nurses with diferent levels of experience. We found that when the turnover rate of senior personnel was minimized, the workload did not decrease. However, when the turnover rate of personnel working in their trial period was reduced to 0, the overall HR turnover and workload decreased. Tis result can be used as a reference for designing salary policies in the medical feld, and it contradicts the line of thinking adopted by current hospital managers. Specifcally, hospital managers attempt   to control HR outfow by promoting senior and advanced personnel. Moreover, they attempt to reduce the contribution of the salaries of primary-level personnel to the overall hospital cost; nevertheless, these personnel constitute a critical group of HRs providing adequate frst-line healthcare in a hospital. Terefore, managers should consider other policy strategies. Figure 7 indicates that reducing the turnover rate of new employees in their trial period is the most efective policy for HR outfow reduction. We did not consider management costs in the fourth simulation. In this simulation, we doubled the number of health-care personnel in the case hospital and then examined the corresponding efect on the workload. Tis examination revealed that the workload increased considerably after a short period. Terefore, the strategy of doubling the number of personnel is unsuitable for reducing HR outfow. Furthermore, as displayed in Figure 8, directly hiring an excessive number of new employees increases communication costs for senior health-care personnel, which in turn increases health-care risks.
Te ffth simulation involved reducing the number of beds, and the simulation results are presented in Figure 9. A reduction in the number of beds had no efect on the nursing workload under the general health-care model. However, when we combined this policy with the policy of increasing the number of health-care personnel (i.e., when we reduced the number of beds while increasing the number of healthcare personnel), the HR outfow decreased. Nevertheless, over the long term, a reduction in the number of beds resulted in increases in the occupancy rate and workload.
Various factors might infuence HRP. Traditionally, predictions regarding the total HRs required in an institution are made on the basis of a single aspect. Te processes adopted by managers in policy-related decision-making are simple, and their thinking can easily become linear. Examining problems involving systematic thinking is difcult. Moreover, SD modeling is highly suitable for HR policy simulations. However, as indicated in this study, the HR outfow of health-care personnel can be infuenced by not only internal factors but also external factors, which include increased medical demand due to population aging in the relevant area, competition between institutions, and NHIA policies (e.g., in Taiwan, nursing fees are part of ward fees and thus receive less attention from managers). Nevertheless, SD modeling can provide some crucial insights. Accordingly, our simulation results are valuable for hospital managers. Te following section describes the simulation results that were obtained by using a simple representation of the developed SD model to emphasize the relationships between the nodes of the stock fow diagram and external related systems.

Policy Simulation Results Obtained with a Macrocosm
Model for the Case Hospital. In the area where the case hospital is located, the demand for medical services has been increasing because of the growth of the elderly population. Moreover, the development of the transportation infrastructure in the area has increased the convenience of traveling, meaning that more people can easily travel to the hospital for medical attention; this has increased personnel workload and thus aggravated the problem of insufcient medical HRs. We conducted a macrocosm simulation of Taiwan's medical resource growth by using a simplifed representation of the designed SD model (Figure 10), in which we combined three objectives: hospital, insurance, and health-care HR systems to the model.   Tree baseline scenarios with diferent rates of population growth and health-care revenues (10%, 20%, and 30% of population increase rate) were designed. Te parameters of the simplifed SD model were determined using statistical information obtained from Taiwan's Directorate General of Budget, accounting and statistics, and open data obtained from the Taiwan Ministry of Health and Welfare. Te parameters of this model are presented in Table 6.
In multiobjective decision-making, the parameters considered (e.g., decisions related to a health-care institution's overall expenses, its insurance costs, and the workload of its care personnel) depend on the decision-maker's preferences. In this study, we assumed that the decisionmaker uses fuzzy language to express uncertain quantities, and we transformed these uncertain quantities into fuzzy numbers. For example, the growth rate for each level of a health-care institution or clinic is between approximately 0.06 and 0.15 (i.e., 0.06 < X i < 0.15, i � 1, 2, 3). Terefore, in this study, all the fuzzy coefcients were assumed to be triangular fuzzy parameters, and a multiobjective model was developed on the basis of the model described in Section 3.4.
Because of constraints related to time and data collection, the scope of the macrocosm simulation was limited to western medicine; thus, data for Chinese medicine and dental medicine were excluded. Diferent solutions were obtained for diferent objective weights (Table 7). Because the frst and second objectives were more important than the third objective, two weight selection methods were used. In the frst method, the importance of the frst and second objectives was emphasized (e.g., cases 1, 2, and 3 adjust the ratio step by step). Moreover, in the second method, the importance of the three objectives was balanced (e.g., case 3 and 4). Last, some extreme cases were also arranged (e.g., cases 5 and 6).
Te macrocosm simulation results are illustrated in Figures 11-14. Te proportion of health-care revenue in cases 1 and 2 changed with time ( Figure 11), similar to the evaluation results obtained in the next case. Moreover, regarding the second objective, an exponential growth was observed in case 5 ( Figure 12). Te proportion of revenue in case 2 was slightly reduced relative to that in case 1; however, the proportion in case 2 increased considerably with time, which indicates that the insurance fee was a sensitive parameter and it alter very fast. If the current industrial structure in Taiwan remains unchanged, the insurance consumption in Taiwan would increase rapidly. In addition, the simulation results obtained when a high weight was assigned to the third objective ( Figure 13) were similar to those obtained when a high weight was assigned to the frst objective. However, the efect of diferent cases strategy was temporary, and the growth curve eventually became smooth. In case 4, the same weight was assigned to the three objectives; hence, we expected the growth rates to be consistent. However, we noted negligible diferences between the simulation results obtained in Cases 4-6 ( Figure 14). Accordingly, the simulation results indicate that adopting a balanced strategy for realizing multiple objectives is advantageous for health institutions.
Finally, we substituted real data into our SD overall model. When we set the same value for the GDP growth rate and population growth rate of Taiwan and considered insurance premiums to be positive, we noted that the required growth rate of the health-care in Taiwan was maintained at approximately 3.813 and that 700 care personnel were added to the workforce (approximately equal to the number of care staf members in a medium-sized medical center). Tis thus led to the achievement of a balance between medical demand and medical supply. Tese results indicate that health-care staf members in Taiwan are being overloaded at work.   Taiwan's NHI program is one of the world's best health insurance systems. A fnancial crisis will still happen if medical expenses get more and more increasing. Terefore, to make the best use of NHI fees, cost-saving policies regarding medical institutions' scales must be implemented. Increases in medical demand and limited income can increase the workload of medical staf members, which could predispose them to emotional risks. Accordingly, we provide the following suggestions for reducing employee workload in hospitals in the same area as the case hospital:

Optimal Distribution of the Level of Care in the
Hospital. Currently, three metropolitan hospitals and fve district hospitals, all of which are acute hospitals, are located in the same area as the case hospital. Tis area has a large population of elderly people, is positioned by the Taiwanese government as a tourism-friendly area, and is suitable for retirement; therefore, the development of diversifed longterm care systems should be promoted in this area on the basis of local residents' characteristics. Te development of a subacute medical care system, such as that in the United States, or an intermediate care system, such as that in the United Kingdom, can reduce the workload of health-care personnel caused by high demands in acute hospitals.

Development of Subsidiary Medical Institutions at
Local Universities to Attract an Increasing Number of Outstanding Talents for Permanent Stay. Te study interviews indicated that many doctors and other health-care personnel of the case hospital use their leave days to take degree courses or to teach in order to obtain a teaching certifcate. In addition to wasting time due to commuting to their learning or teaching venues, these employees leave the case hospital after they obtain their degree. Terefore, to resolve this problem, subsidiary medical institutions can be established in local universities.

Promotion of Health and Improvement of Self-Care
Capabilities among Elderly People. Te interview results indicated that in the area where the case hospital is located, changes in family structures have forced many of the elderly people to live alone, which can negatively infuence their healing. Te hospitals in the area should cooperate with social workers to develop diversifed health promotion programs for improving residents' health awareness, health literacy, and self-care. Such programs can reduce the medical demand.

Development of Integrated Information Platforms and
Automatic Delivery Systems. Improving employees' work efciency is the most efective strategy for reducing the pressure related to HR costs caused by increased medical demands. Te central government can encourage hospitals in the considered area to increase their overall work efciency through measures such as fnancial support, supporting policies, and incentive mechanisms. For example, the computerization of medical record systems can improve work efciency. Data and interfaces from diferent systems should be continually integrated. Moreover, the hospitals in this area can develop a personalized health platform for residents, which can enable them to identify more people in need of medical services. Tey can apply the capitation payment system to reduce the overall medical demand. Te automatic delivery system used in the case hospital can be adopted in other hospitals in the area to reduce employees' workload.

Conclusions and Managerial Implication
Because of advances in various forms of media, the information asymmetry between doctors and patients has decreased. However, disputes often occur between health-care personnel and patients, which can create mental pressure for health-care personnel and result in HR outfow from medical institutions. Nearly all hospitals in Taiwan are covered by the NHI program; thus, their income is limited. However, medical demands are increasing because Taiwan's elderly population is growing. In addition to medical centers and university hospitals, small and medium-sized hospitals are facing the problem of HR outfow. Tis phenomenon is most commonly observed among nursing staf members, for whom the workload is high but the salary is low.
Managers usually modify the HR policies of their medical institutions through trial-and-error approaches to overcome the problem caused by nursing personnel turnover. Such trial-and-error approaches can lead to the failure of HR policies, resulting in the waste of money and other resources. To overcome this problem, this study developed an SD model to simulate the efects of various HR strategies in a case hospital in diferent scenarios. Moreover, we constructed an SD-integrated MOP model to simulate the long-term efects of diferent HR strategies in the case hospital under various scenarios. Tis model can assist HR policymakers in medical institutions to achieve trade-ofs between diferent objectives when attempting to reduce HR outfow.
Tis study has some limitations. First, data were collected from only one hospital. Te scale of the developed model was reduced to cover only the feld of HRs. Future studies can investigate hospitals of diferent levels and examine the diferent strategies resulting in fndings between long-term care institutions and general hospitals. Moreover, the workload-related system developed for health-care staf in this study is a preliminary framework for controlling their workload. However, under the NHI system, the NHI system is more favorable to institutions that are already at a stronger position. Future studies can consider factors related to external competition from other hospitals to determine whether such factors lead to an unnatural distribution of HRs; the fndings of such studies can serve as a reference for the establishment of policies in relevant institutions. Tird, only fuzzy uncertainty was considered in the developed MOP model. Future studies can consider other types of uncertainty, such as stochastic uncertainty, to examine additional risk factors for HR outfow.

Data Availability
Te data used to support the fnding of this study are included within the article.

Conflicts of Interest
Te authors declare that there are no conficts of interest regarding the publication of this paper.